Integrand size = 18, antiderivative size = 18 \[ \int \frac {\sqrt [3]{a+a \cosh (c+d x)}}{x} \, dx=\text {Int}\left (\frac {\sqrt [3]{a+a \cosh (c+d x)}}{x},x\right ) \]
[Out]
Not integrable
Time = 0.05 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\sqrt [3]{a+a \cosh (c+d x)}}{x} \, dx=\int \frac {\sqrt [3]{a+a \cosh (c+d x)}}{x} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {\sqrt [3]{a+a \cosh (c+d x)}}{x} \, dx \\ \end{align*}
Not integrable
Time = 2.55 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.11 \[ \int \frac {\sqrt [3]{a+a \cosh (c+d x)}}{x} \, dx=\int \frac {\sqrt [3]{a+a \cosh (c+d x)}}{x} \, dx \]
[In]
[Out]
Not integrable
Time = 0.02 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.89
\[\int \frac {\left (a +a \cosh \left (d x +c \right )\right )^{\frac {1}{3}}}{x}d x\]
[In]
[Out]
Exception generated. \[ \int \frac {\sqrt [3]{a+a \cosh (c+d x)}}{x} \, dx=\text {Exception raised: TypeError} \]
[In]
[Out]
Not integrable
Time = 1.64 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83 \[ \int \frac {\sqrt [3]{a+a \cosh (c+d x)}}{x} \, dx=\int \frac {\sqrt [3]{a \left (\cosh {\left (c + d x \right )} + 1\right )}}{x}\, dx \]
[In]
[Out]
Not integrable
Time = 0.34 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {\sqrt [3]{a+a \cosh (c+d x)}}{x} \, dx=\int { \frac {{\left (a \cosh \left (d x + c\right ) + a\right )}^{\frac {1}{3}}}{x} \,d x } \]
[In]
[Out]
Not integrable
Time = 0.51 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {\sqrt [3]{a+a \cosh (c+d x)}}{x} \, dx=\int { \frac {{\left (a \cosh \left (d x + c\right ) + a\right )}^{\frac {1}{3}}}{x} \,d x } \]
[In]
[Out]
Not integrable
Time = 1.70 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {\sqrt [3]{a+a \cosh (c+d x)}}{x} \, dx=\int \frac {{\left (a+a\,\mathrm {cosh}\left (c+d\,x\right )\right )}^{1/3}}{x} \,d x \]
[In]
[Out]